Best Known (31, 31+38, s)-Nets in Base 4
(31, 31+38, 38)-Net over F4 — Constructive and digital
Digital (31, 69, 38)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 24, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (7, 45, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (5, 24, 17)-net over F4, using
(31, 31+38, 43)-Net in Base 4 — Constructive
(31, 69, 43)-net in base 4, using
- t-expansion [i] based on (30, 69, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
(31, 31+38, 60)-Net over F4 — Digital
Digital (31, 69, 60)-net over F4, using
- net from sequence [i] based on digital (31, 59)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 31 and N(F) ≥ 60, using
(31, 31+38, 390)-Net in Base 4 — Upper bound on s
There is no (31, 69, 391)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 350356 076073 552752 268275 855850 482695 597312 > 469 [i]